Within the supersymmetry scheme including many-body interactions, identical superdeformed (SD) bands and DeltaI = 4 bifurcation in A similar to 130 mass region are investigated systematically. Quantitatively good results for the gamma -ray energy (E gamma) spectra, dynamical moments of inertia, and energy differences DeltaE(gamma)-Delta (ref)(gamma) are obtained. This shows that the supersymmetry approach is quite powerful in describing not only generic rotational properties, but also DeltaI=4 bifurcation and identical SD bands simultaneously. Meanwhile, the DeltaI=4 bifurcation may come from the perturbation with SO(5) [or SU(5)] symmetry on the rotational symmetry.